Question

One positive number is two more than twice another. If their product is 60, find the numbers.

Answer 1

The first number is 5, and the other number is 12

Explanation:

1st Number = n

2nd number = 2n +2

1st Number * 2nd Number =60

n(2n+2)=60

2n^2 + 2n =60

2n^2 +2n -60 = 0

Factor Out:

2(n-5)(n+6) = 0

n-5 = 0 n+6 = 0

n = 5 n = -6

n = -6 wont make sense so n =5 would be the answer

Check:

5(10+2) =60

5(12)= 60

60 = 60

Answer 2

The smaller number is 5 and the larger number is 12.

Let x be the smaller number. Then the larger number is 2x + 2. We know that their product is 60, so we can write the equation:

x(2x + 2) = 60

Expanding the left side of the equation, we get:

2x^2 + 2x = 60

Moving all the terms to one side, we get:

2x^2 + 2x - 60 = 0

Dividing both sides by 2, we get:

x^2 + x - 30 = 0

Factoring the left side of the equation, we get:

(x + 6)(x - 5) = 0

Therefore, x = -6 or x = 5. Since x is a positive number, the smaller number is 5 and the larger number is 2(5) + 2 = 12.